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a Earth and Environmental Sciences, Lawrence Livermore National Laboratory, P.O. Box 808, L-202, Livermore, CA 94550
b Dep. of Hydrodynamics and Water Resources, Technical University of Denmark
Corresponding author (wildenschild1{at}llnl.gov)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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(h), and the unsaturated hydraulic conductivity characteristic, K(h). Commonly, these characteristics are measured under static equilibrium or steady-state conditions and are subsequently applied to both steady-state and transient flow analyses, thereby assuming that the retention characteristic is not affected by nonequilibrium conditions. Thus, both equilibrium and steady-state measurements are routinely used to analyze transient flow phenomena and vice versa. However, a number of experiments presented in the sixties and early seventies suggested that these assumptions might not be entirely justifiable. When comparing drying water retention data obtained by equilibrium, steady state, and transient methods, Topp et al. (1967) found that more water was retained in a sand at a given matric potential for the transient flow case than for the static equilibrium and steady-state cases. The authors referred to a study by Harris and Morrow (1964), who studied pendular rings in packs of relatively large uniform spheres, and found that some of the pores in the drained sphere pack remained full, as these became isolated from the bulk liquid before their air-entry pressure was attained. This bypassing of isolated liquid-filled pores explained the observed higher retained water content. An analogous explanation was suggested by Davidson et al. (1966) who investigated the dependence of the retention characteristic on the applied pressure increment during wetting. They reported a noticeable dependence of the equilibrium water content on the size of the applied pressure increment such that a higher water content was measured when small pressure increments were used during water absorption. The increase in water content was attributed to a reduction in the air volume entrapped during absorption if the soil was wetted at a slower rate. The authors concluded that the changes in water content should be treated as an immiscible displacement process, where the resistance to movement and spatial configuration of both water and air need not be single valued with respect to water content—a hypothesis stated previously by Nielsen et al. (1962).
Later, Smiles et al. (1971) carried out desorption experiments in a horizontal column of uniform soil and found that the relationship between the soil water matric potential and the water content was nonunique throughout the column. Vachaud et al. (1972) continued the work of Smiles et al. (1971) to determine if this same phenomenon occurred in vertical drainage of a uniform column of fine sand as well. They compared retention curves obtained under static and dynamic flow conditions and their results were consistent with those of Smiles et al. (1971). In particular, Vachaud et al. (1972) showed that a rate increase of matric potential with time reduced the volumetric outflow, thereby causing deviations from the static retention characteristic.
The issues of rate dependence of soil hydraulic properties have since been mostly disregarded. The unsaturated hydraulic conductivity dependence on flow conditions in particular has been the focus of few investigations, partly because of the tedious nature of its measurement; however, recent experiments carried out by Wildenschild et al. (1997), Plagge et al. (1999), Hollenbeck and Jensen (1999), and Schultze et al. (1999) support the notion that the flow regime may vary notably between different types of experiments, thereby influencing the estimation of the unsaturated hydraulic properties. In addition to the water retention characteristic, Plagge et al. (1999) investigated the influence of both flow rate and boundary condition type on the hydraulic conductivity function and concluded that experiments with larger water potential gradients tended to increase the unsaturated hydraulic conductivity. In experiments designed to investigate the influence of pore scale dead-end air fingers on relative permeabilities for air sparging in soils, Clayton (1999) found that the measured air permeabilities decreased with increasing displacement rate. Clayton attributed the displacement-rate dependent behavior to the development and subsequent breakthrough of dead-end air fingers. Most recently, Friedman (1999) concluded that the influence of flow velocity on the solid–liquid–gas contact angle could also explain the phenomena observed by Topp et al. (1967).
With the introduction of new and faster techniques for transient measurement of the hydraulic characteristics such as the one-step (Kool et al., 1985) and multi-step (van Dam et al., 1994; Eching et al., 1994) outflow methods, the question of the validity of these measurements has since become increasingly important. As many researchers now apply these faster techniques to determine the hydraulic characteristics of soils, it is important to examine the influence of the boundary conditions on the measurement results for these experiments. In many cases, recorded data of cumulative outflow as a function of time is combined with soil water matric potential head measured with a tensiometer at a point inside the sample (Eching et al., 1994) to facilitate inverse estimation of the hydraulic parameters. If the water content is dependent not only on the matric potential, but is also influenced by outflow rate, it needs to be taken into consideration when estimating the soil hydraulic properties. Outflow procedures are, however, not the only methods to be affected by this phenomenon. For the traditional static methods such as the pressure plate extraction method (Klute, 1986), soil water retention may be a function of the rate of flow between equilibrium points as well.
As improvements in measurement techniques, as well as the implementation of dynamic measurement methods, have become available, the aim of the present study was to continue the above referenced work. Using the currently available improved measurement techniques, we investigated the rate dependence of unsaturated hydraulic characteristics for two soils in short laboratory columns. Thus, the objective of this study was to investigate the influence of flow rate on soil hydraulic characteristics using both a direct and an inverse estimation method for two soils with different pore size distributions. The direct estimation is based on Darcy's Law (steady state), while the inverse estimation relies on numerical solution of Richards' equation and as such is a transient approach.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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2 cm into the sample. Two 15-psi transducers (136PC15G2, Honeywell, Minneapolis, MN) were used to monitor the matric potential head at the two locations. In addition, a 1-psi differential transducer (26PCAFA1D, Honeywell, Minneapolis, MN) was mounted to monitor the difference in matric potential between the two tensiometers, thus allowing computation of the hydraulic gradient. Two additional ports were added on opposite sides of the cell to vent the sample with CO2 and allow full water saturation at the start of the outflow experiment.
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7.0 x 10-6 cm/s, the hydraulic resistance of the thin nylon membrane was low compared with other commonly used porous membranes, thereby minimizing water pressure differences across the porous membrane during drainage of the soil core. The experiments were conducted for two soils of varying textural composition, a Lincoln sand obtained from the EPAs RS Kerr Environmental Research Laboratory in Ada, OK, and a Columbia fine sandy loam collected along the Sacramento River near West Sacramento, CA. Soil properties for both soils are listed in Table 1 (Liu et al., 1998). The Columbia and Lincoln soil were sieved through 0.5- and 0.6-mm sieves, respectively, prior to packing. Each sample was packed only once for each series of experiments to minimize packing effects on the results. The soil was packed in the pressure cell in small increments and the cell tapped between each successive addition. Initial experiments with the Columbia soil showed some settling after a few wetting and drying cycles; therefore, the Columbia soil sample was vibrated for 1/2 hour after packing to obtain a well-settled sample.
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All experiments were started at an initial condition of hbottom -2 cm. Prior to each drainage experiment, the soil samples were resaturated using the same procedure every time (including the use of CO2 to dissolve trapped air) to maintain identical initial saturation values between the different drainage experiments. Otherwise, observed differences could be attributed to varying initial conditions. The standard deviations of the initial sample weights representing variations of initial saturation were 0.962 g for six replicates of the Columbia soil and 0.732 g for 10 replicates of the Lincoln soil, representing water content variations of 0.0075 and 0.0050 cm3 cm-3 for the Lincoln soil and the Columbia soil, respectively.
Direct Estimation Using Darcy's Law
The retention characteristics for the soils were established from the average of the two tensiometer readings and the measured cumulative outflow volumes. The cumulative outflow was converted to sample average water content using soil porosity and assuming initial fully saturated conditions. At the conclusion of each experiment, the sample was weighed to determine final water content values, from which initial water content values were verified. This approach may introduce potential errors, since the measurements were carried out during transient conditions, thereby leading to possible depth variations in matric potential head, while a single core averaged water content was estimated from the cumulative outflow data. This could be of particular concern for the fast, one-step experiments where depth dependent matric potential head gradients are most likely to occur. Also, the presence of the tensiometers in the sample could cause some disturbance of the flow field. As mentioned earlier, we believe that the small size and the offsetting of the tensiometers justify the assumption of one dimensionality.
The unsaturated hydraulic conductivity was estimated directly from Darcy's Law using various computational procedures. The tensiometer pair provided the hydraulic gradient in the center of the soil core as a function of drainage time, and when combined with the outflow rate provided the unsaturated hydraulic conductivity as a function of matric potential head or volumetric water content. To account for water flux density differences between the upper and lower parts of the soil sample during outflow, we used the method of Wendroth et al. (1993) to estimate the unsaturated hydraulic conductivity.
The soil sample was divided into three compartments as outlined in Fig. 2
. The first (top) compartment (l1) extended between the surface of the soil sample and the center between the two tensiometers, and was represented by the matric potential head measured in the first (top) tensiometer, h1. The second compartment (l2) extended from the center between the two tensiometers to the center between the lower tensiometer and the bottom of the soil sample. This second compartment was represented by the matric potential head measured with the second (lower) tensiometer, h2. The third compartment (l3) was defined by the bottom of the soil sample and the center between the lower tensiometer and the bottom of the sample. The matric potential head between the bottom of the sample and the lower tensiometer was assumed to be linearly distributed. Thus, this compartment was represented by the weighted mean of the matric potential head within the compartment 
. For each compartment, the water content at each time step was calculated from the representative matric potential head values (i.e., 1, 2, and 3).
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) or K(h), the fluxes between the compartments were computed in two ways: either (1) from the top to the bottom, or (2) from the bottom to the top.1, while the fluxes between compartments 2 and 3 (q23) were computed from time rate of water storage changes using 1 and 2. Subsequently, K12(h) and K23(h) or K12() and K23() were estimated, assuming the Darcy equation to be valid, while substituting the representative matric potential head values (h1 and h2 for q12, and h2 and h3 for q23). Finally, K3 values were calculated directly from the bottom compartment drainage rate and matric potential gradients. 1, 2, and 3), and using the appropriate matric potential gradients. To simplify the direct estimation results, we will only present data using a selection of experiments and conductivity estimations for each soil. For the Lincoln soil these experiments are one-step (0–250 mbar and 0–125 mbar), multistep (0–50–100 mbar and 0–25–35–62–80–100 mbar) and the quasi-static experiment. For the Columbia soil, we are presenting estimated data for one-step (0–500 mbar), multistep (0–250–500 mbar and 0–125–250–375–500 mbar), and the quasi-static experiment. In addition, we have chosen only to present data for the middle (K23 and K32) and lower part (K3) of the sample. This was done partly for simplicity, but also because the estimates from the upper part (K12 and K21) were affected by the large gradients present towards the end of the experiments. For the multistep experiments in particular, this meant that the curves were discontinuous between individual pressure steps. Also, the estimates from the middle part of the sample (K23 and K32) provide a more correct basis for comparison with the estimates based on the drainage rate (K3), as opposed to the estimates from the upper part of the sample (K12 and K21).
Unfortunately, it was not possible to estimate the hydraulic conductivity from the syringe pump experiments because the very small hydraulic gradients prevented accurate K estimation.
Inverse Estimation Based on Richards' Equation
The unsaturated hydraulic properties were inversely estimated using HYDRUS-1D (Simunek et al., 1998), which numerically solves Richards' equation in one dimension using a Galerkin-type linear finite element scheme. Minimization is accomplished using the Levenberg-Marquardt nonlinear weighted least squares approach. The objective function was defined as the average weighted squared deviation normalized by the measurement variances of particular measurement sets. For additional details about inverse modeling, its application for estimation of soil hydraulic properties and the definition of the objective function, refer to Simunek et al. (1998), and Hopmans and Simunek (1999). For these experiments, the objective function contained matric potential head readings for the two tensiometers and cumulative outflow data measured as a function of time. The expressions of van Genuchten (1980) were used to parameterize the hydraulic functions
 | (1) |
s, r and are full, residual and actual water contents, 
, n and l are constants, 
, 
is matric potential, and K and Ks are unsaturated and saturated hydraulic conductivities. The parameters optimized were either (, n, Ks, r) or (, n, Ks, r, l) where l is the exponent in Mualem's (1976) equation. The exponent is commonly fixed at a value of 0.5, however, the fit to the data was improved if the l parameter was optimized as well. The saturated water contents (s) were fixed at 0.37 and 0.45 cm3 cm-3 for the Lincoln and Columbia soils, respectively. The unsaturated hydraulic conductivity was not fixed at its measured value in the optimizations because the inverse solutions converged readily without Ks data. The variation in optimized Ks values (Table 2 and 3) is less than an order of magnitude, and as such could not be improved with a laboratory Ks measurement, which usually has an estimation error of similar magnitude. Also, we were interested in investigating dynamic phenomena, so including Ks data measured at steady-state conditions might confuse the issue.
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values with decreasing flow rate, while the optimized n values are less sensitive to the flow rate. The increase in n values is not seen for the Columbia soil. These inversely obtained results reflect the trends observed for the other estimation methods, which are discussed in the following. |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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7% by volume for a given matric potential in the early stages of the experiment. As we progress from the highest (0–250 mbar) to the lowest (quasi-static) flow rate, we also note a decrease in the measured air-entry value of 15 cm. Similar trends can be observed in the inversely estimated curves, suggesting that the directly estimated (measured) curves are representative of the average behavior of the sample. In contrast, no apparent rate dependence was observed for the fine textured Columbia soil (Fig. 4a–e)
. Generally, our measured curves for both the Lincoln and Columbia soil compare favorably with the curves measured by Chen et al. (1999).
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Physical Processes Controlling Outflow
A number of different physical processes might contribute to the rate-dependent results observed in our experiments. We suggest the following processes or a combination thereof, which systematically can explain the observed phenomena.
85%, because of the general disconnection of the gas phase at these high saturations. Consequently, one would expect nonunique soil water retention curves, controlled by imposed boundary conditions and pore connectivity characteristics.
Observed Phenomena in the Context of the Suggested Processes
We suggest that the marked effect on the curves for the Lincoln soil can be attributed to three or four of the above stated mechanisms. The first mechanism is caused by disconnection of flow paths at higher flow rates, so that water is being trapped in dead-end pore space, Process 1. For the low-pressure outflow experiments, water in individual pores remains connected to the bulk water, thereby allowing water to drain as the water potential decreases during multi-step outflow experiments. A similar explanation has been suggested earlier by Smiles et al. (1971) and Topp et al. (1967).
In addition to water entrapment, we believe that Processes 2, 3 and 4 contribute to the measured rate-dependent soil hydraulic characteristics. Initial drainage of the lower part of the sample (Process 2) was observed in one-step outflow experiments using x-ray computer assisted tomography (CT) by Hopmans et al. (1992) and we are currently observing similar patterns in preliminary x-ray CT experiments of the Lincoln soil. This mechanism is enhanced for soils with a narrow pore-size distribution, and hence is expected to be more pronounced for the sandy Lincoln soil. Similarly, the air-entry value effect (Process 4) is likely to influence our results, since the air entry value of the Lincoln soil is -20 cm; that is, drainage occurs only if matric potential head values are smaller than -20 cm; however, the initial condition of the soil was only -2 cm, so that the first pressure increment was applied when the Lincoln soil was still saturated. This is particularly critical for the Lincoln soil experiments with large pressure increments (one or two steps) where early drainage most likely did not conform to Richards type of flow, which assumes that the nonwetting or air phase is continuous throughout the soil sample (Hopmans et al., 1992). Also, Schultze et al. (1999) stated that the air phase is discontinuous during drainage until a significant amount of water has left the pore system and an emergence point saturation is reached, at which point the gas permeability jumps to a finite value.
The influence of flow rate on the retention characteristic was not apparent for the finer textured Columbia soil (Fig. 4a–e) using different applied pressures; however, we hypothesize that a similar behavior might have occurred if much higher gas pressures had been applied to drain the Columbia soil than used in the reported experiments. Chen et al. (1999) showed that the air permeability is higher for the Columbia soil than for the Lincoln soil, at the same degree of saturation. Therefore, some of the above processes, which are controlled by the low air permeability and the lack of air phase continuity of the Lincoln soil, might not be of importance for the Columbia soil. Another reason for the relatively small deviations among the retention curves for the Columbia soil, could be the small matric potential gradients present later in the experiment (i.e., at lower saturations). Fig. 7 and 8
illustrate matric potential gradients as estimated directly from the two tensiometers for the Lincoln and Columbia soils, respectively. As seen from Fig. 8, the directly estimated matric potential gradients in the Columbia soil (solid lines) are large at first following an applied pressure increment, but quickly drop to -1.0, as is expected if hydraulic equilibrium is attained. The periodic return of the matric potential gradients to near zero for the Columbia soil is the result of the total soil water potential approaching static conditions after each of the applied pressure increments; however, the return to static equilibrium after each applied pressure increment does not always occur for the sandy soil, especially not for the high-pressure single step experiments as illustrated in Fig. 7. The continuously increasing matric potential gradient (solid lines) is indicative of a soil water regime not tending towards static equilibrium. Our proposed mechanism, Process 2, can explain this phenomenon. After a large pressure increment is applied, the bottom section of the sandy soil is drained, thereby emptying the largest, highly conductive pores. For a soil with a narrow pore size distribution (Lincoln soil), drainage of the largest pores prevents continued drainage and equilibration of the soil above the initially drained portion, and effectively results in the increasing total water potential gradients with progressing drainage as observed in Fig. 7. For the two slower outflow experiments (0–50–100 mbar and 0–25–35–62–80–100 mbar), a similar behavior as for the finer textured soil is observed, and the gradients return to unity, shortly after the pressure step is applied.
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83 days have passed (see inset of Fig. 7). Generally, when performing retention curve measurements on sandy materials it is assumed that these can be done relatively fast, whereas the more clayey materials require time-consuming experiments; however, our results indicated otherwise. At low saturations, we observed low unsaturated hydraulic conductivities for the fast outflow experiments for the Lincoln soil, Fig. 5e and Fig. 5f. We suggest that this is due to water being either trapped (Process 1) or blocked from the main water body (Process 2), thereby becoming immobile and effectively not contributing to flow. We hypothesize that this water becomes entrapped and immobile in the early stages of the experiment when relatively high flow rates prevail, particularly in those experiments where large one-step pressure steps were used to induce outflow. In Fig. 9 , the cumulative outflow volumes are plotted as a function of time for the Lincoln soil, showing that the maximum flow rates occur initially when the first pressure increment is applied. We assume that these maximum flow rates occur near the nylon membrane at the bottom of the sample. Specifically, the 0–250 and 0–125 drainage experiments induce these high flow rates in the first few minutes of the experiment (see inset of Fig. 9). The initially trapped or blocked water will remain trapped as the soil continues to drain because it is disconnected from the flowing water phase. Another possible reason for the negligible effect of the outflow rate on the hydraulic characteristics of the Columbia soil is its dominance of smaller pores following our proposed Process 1. Single water-filled pores are less likely to be isolated from the main flow path in the Columbia soil, compared with the coarser textured Lincoln soil.
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0.20 cm3 cm-3. The inversely estimated data is based on the assumption of Richards flow and air phase continuity, which could be the cause of this difference between the direct and indirect unsaturated hydraulic conductivity calculations. The crossover of the hydraulic conductivity curves is not observed for the finer textured Columbia soil in Figure 6e, likely due to its more poorly defined air-entry value (Process 4), wider pore-size distribution (Process 1 and 2), and higher air permeability (Process 3). Also, the measurements of the finer-textured Columbia soil do not show the continuously increasing nonequilibrium gradients as measured for the Lincoln soil (compare Fig. 7 and 8), and therefore the hydraulic characteristics of this soil are less likely to be dependent on flow rate. The lower initial flow rates and their smaller variation among the Columbia experiments are illustrated in Fig. 10 (note that the inset is plotted on the same scale for the two soils).
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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-35 cm. In the experiments of Smiles et al. (1971), air access was secured at any time because the sample holder included ventilation holes. However, their experiments confirm Process 1 to be effective. Water retention is highest closest to the water inlet (largest fluxes) and for experiments with the largest head gradients (Fig. 4 and 6). The results of Smiles et al. (1971) were confirmed by Vachaud et al. (1972), who showed that the largest deviations from the static water retention curve occur when large head gradients are applied (Process 1 and 2). Based on our investigation it is critical to consider the method by which the hydraulic properties for unsaturated soils are determined, thus keeping in mind the purpose of the characterization. For the coarse textured Lincoln soil we have shown that the use of hydraulic parameters obtained under relatively high outflow conditions may not accurately represent slow flow phenomena, as mostly experienced in the field. The lack of static equilibrium in the coarser soil material may affect both inverse and direct estimations. Therefore, the choice of boundary conditions and estimation method must be carefully evaluated.
The rate dependence of the hydraulic characteristics has been shown to be of less importance for the finer textured Columbia soil, at least for the experimental conditions investigated in this study. The higher air permeability for the Columbia soil at a given saturation, along with its wider pore-size distribution and a more poorly defined air entry value are likely reasons for the lack of rate dependence observed for the Columbia soil. Also, the induced flow rates in the Columbia soil experiments were not as high as those measured for the Lincoln soil. Therefore, it is possible that some of the flow rate effects on the soil hydraulic characteristics are effective for the Columbia soil as well, if higher flow rates were used by applying much larger water pressure gradients than used in this study.
We realize that other processes such as those stated for instance by Demond and Roberts (1991), Hassanizadeh and Gray (1993), Clayton (1999), and Friedman (1999) may also be contributing to the observed flow rate dependent soil hydraulic properties. Regardless, ignoring these rate-dependent phenomena might lead to significant errors, especially in situations where hydrological models are used with hydraulic parameters that are obtained at considerably different flow rates.
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ACKNOWLEDGMENTS |
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Received for publication January 25, 2000.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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